5 papers
String algebras over local rings: regular examples
Raphael Bennett-Tennenhaus
String algebras, in the usual sense, are finite-dimensional algebras over a given ground field. We recall a generalisation of the definition of a string algebra, which was introduc…
Classification of modules for complete gentle algebras
Raphael Bennett-Tennenhaus
We classify finitely generated modules over a class of algebras introduced in the authors' Ph.D thesis, called complete gentle algebras. These rings generalise the finite-dimension…
Characterisations of -pure-injectivity in triangulated categories and applications to endoperfect objects
Raphael Bennett-Tennenhaus
We provide various ways to characterise -pure-injective objects in a compactly generated triangulated category. These characterisations mimic analogous well-known results from t…
-pure-injectives in homotopy categories for gentle algebras
Raphael Bennett-Tennenhaus
We consider the homotopy category of complexes of projective modules over any gentle algebra. We prove that indecomposable -pure-injective objects in s must be shifts of string…
-pure-injective modules for string algebras and linear relations
Raphael Bennett-Tennenhaus, William Crawley-Boevey
We prove that indecomposable -pure-injective modules for a string algebra are string or band modules. The key step in our proof is a splitting result for infinite-dimensional li…